To help you solve the problem, let's break it down step by step.
First, let's clarify the given information:
- Original cost of the car: $21,000
- Down payment: $1,000
- Loan period: 5 years (which means 60 monthly payments)
- Monthly interest rate: 0.0625% or 0.000625 (since it's given as a percentage)
Now, let's calculate the monthly payment (PMT) using the formula you provided:
Pn = PMT * (1 - (1 + i)^-n / i)
Substituting the given values:
Pn = PMT * (1 - (1 + 0.000625)^-60 / 0.000625)
Now, let's simplify the equation further:
Pn = PMT * (1 - (1.000625)^-60 / 0.000625)
To solve for PMT, divide both sides of the equation by the expression [(1.000625)^-60 / 0.000625]:
PMT = Pn / (1 - (1.000625)^-60 / 0.000625)
Now, let's plug in the values and calculate the monthly payment amount for the car loan:
PMT = 20,000 / (1 - (1.000625)^-60 / 0.000625)
= 20,000 / (1 - 0.96103514)
Simplifying further:
PMT = 20,000 / 0.03896486
≈ 513.19
So, the monthly payment on the 5-year car loan, to the nearest cent, is approximately $513.19.
For the second part of the question, you have the same formula but with a different value. Let's calculate it:
PMT = 300 / (1 - (1.000625)^-60 / 0.000625)
= 300 / (1 - 0.96103514)
= 300 / 0.03896486
≈ 7,694.21
So, the monthly payment for the second part of the question is approximately $7,694.21.
Make sure to double-check the values you are entering into your calculator, as errors often occur due to mistyped numbers or misplaced decimal points.